The parallel parking problem is a motion planning

Motion planning

Motion planning is a term used in robotics for the process of detailing a task into discrete motions....

 problem in control theory

Control theory

Control theory is an interdisciplinary branch of engineering and mathematics that deals with the behavior of dynamical systems. The desired output of a system is called the reference...

 and mechanics

Mechanics

Mechanics is the branch of physics concerned with the behavior of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment....

 to determine the path a car must take in order to parallel park

Parallel parking

thumb|250px|right|Parallel-parked cars in [[Washington, D.C.]]thumb|250px|right|A motorist gets assistance parallel-parkingParallel parking is a method of parking a vehicle in line with other parked cars. Cars parked in parallel are in one line, parallel to the curb, with the front bumper of each...

 into a parking space. The front wheels of a car are permitted to turn, but the rear wheels must stay fixed. When a car is initially adjacent to a parking space, to move into the space it would need to move in a direction perpendicular to the allowed path of motion of the rear wheels. The admissible motions of the car in its configuration space are an example of a nonholonomic system

Nonholonomic system

A nonholonomic system in physics and mathematics is a system whose state depends on the path taken to achieve it. Such a system is described by a set of parameters subject to differential constraints, such that when the system evolves along a path in its parameter space but finally returns to the...

.